Central Configurations and Mutual Differences
Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is t...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148595 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Central Configurations and Mutual Differences / D.L. Ferrario // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862549111874519040 |
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| author | Ferrario, D.L. |
| author_facet | Ferrario, D.L. |
| citation_txt | Central Configurations and Mutual Differences / D.L. Ferrario // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is the orthogonal projection over the spaces of 1-cocycles and Ψ(q)=q/|q|α+2. It is shown that differences qij of central configurations are critical points of an analogue of U, defined on the space of 1-cochains in the Euclidean space E, and restricted to the subspace of 1-cocycles. Some generalizations of well known facts follow almost immediately from this approach.
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| first_indexed | 2025-11-25T20:36:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148595 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:36:33Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ferrario, D.L. 2019-02-18T16:25:23Z 2019-02-18T16:25:23Z 2017 Central Configurations and Mutual Differences / D.L. Ferrario // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37C25; 70F10 DOI:10.3842/SIGMA.2017.021 https://nasplib.isofts.kiev.ua/handle/123456789/148595 Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is the orthogonal projection over the spaces of 1-cocycles and Ψ(q)=q/|q|α+2. It is shown that differences qij of central configurations are critical points of an analogue of U, defined on the space of 1-cochains in the Euclidean space E, and restricted to the subspace of 1-cocycles. Some generalizations of well known facts follow almost immediately from this approach. Work partially supported by the project ERC Advanced Grant 2013 n. 339958 “Complex Patterns for Strongly Interacting Dynamical Systems COMPAT”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Central Configurations and Mutual Differences Article published earlier |
| spellingShingle | Central Configurations and Mutual Differences Ferrario, D.L. |
| title | Central Configurations and Mutual Differences |
| title_full | Central Configurations and Mutual Differences |
| title_fullStr | Central Configurations and Mutual Differences |
| title_full_unstemmed | Central Configurations and Mutual Differences |
| title_short | Central Configurations and Mutual Differences |
| title_sort | central configurations and mutual differences |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148595 |
| work_keys_str_mv | AT ferrariodl centralconfigurationsandmutualdifferences |